The adaptive optics system (AO) without a wavefront sensor produces an alternative tool to correct the aberrations where the wavefront distortions are hard to be measured directly. This kind of adaptive optics system optimizes an evaluation parameter directly relevant to the wavefront quality to achieve the wavefront correction, and the optimization algorithms determines the efficiency of wavefront sensor-less AO system. In this paper, several frequently-used algorithms covering hill climbing algorithm, genetic algorithm, simulated annealing algorithm and two hybrid algorithms, known as hybrid genetic-hill climbing algorithm and hybrid simulated annealing-hill climbing algorithm (SAHC), have been investigated to improve the correction efficiency. The correction speeds and correction effects of the five kinds of algorithms have been compared in simulations and experiments for an adaptive optics system with 19-elements unimorph deformable mirror. The results show that hill climbing algorithm has the fastest correction speed, but suffered from the local optimum problem. The other four kinds of algorithms can get good correction results and have similar correction effects. Considering the correction effect and correction speed comprehensively, SAHC is the most efficient optimization algorithm in the five kinds of optimization algorithms.